Integrate a Laguerre series. Returns the Laguerre series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear chang
(c, m=1, k=[], lbnd=0, scl=1, axis=0)
| 675 | |
| 676 | |
| 677 | def lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0): |
| 678 | """ |
| 679 | Integrate a Laguerre series. |
| 680 | |
| 681 | Returns the Laguerre series coefficients `c` integrated `m` times from |
| 682 | `lbnd` along `axis`. At each iteration the resulting series is |
| 683 | **multiplied** by `scl` and an integration constant, `k`, is added. |
| 684 | The scaling factor is for use in a linear change of variable. ("Buyer |
| 685 | beware": note that, depending on what one is doing, one may want `scl` |
| 686 | to be the reciprocal of what one might expect; for more information, |
| 687 | see the Notes section below.) The argument `c` is an array of |
| 688 | coefficients from low to high degree along each axis, e.g., [1,2,3] |
| 689 | represents the series ``L_0 + 2*L_1 + 3*L_2`` while [[1,2],[1,2]] |
| 690 | represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + |
| 691 | 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. |
| 692 | |
| 693 | |
| 694 | Parameters |
| 695 | ---------- |
| 696 | c : array_like |
| 697 | Array of Laguerre series coefficients. If `c` is multidimensional |
| 698 | the different axis correspond to different variables with the |
| 699 | degree in each axis given by the corresponding index. |
| 700 | m : int, optional |
| 701 | Order of integration, must be positive. (Default: 1) |
| 702 | k : {[], list, scalar}, optional |
| 703 | Integration constant(s). The value of the first integral at |
| 704 | ``lbnd`` is the first value in the list, the value of the second |
| 705 | integral at ``lbnd`` is the second value, etc. If ``k == []`` (the |
| 706 | default), all constants are set to zero. If ``m == 1``, a single |
| 707 | scalar can be given instead of a list. |
| 708 | lbnd : scalar, optional |
| 709 | The lower bound of the integral. (Default: 0) |
| 710 | scl : scalar, optional |
| 711 | Following each integration the result is *multiplied* by `scl` |
| 712 | before the integration constant is added. (Default: 1) |
| 713 | axis : int, optional |
| 714 | Axis over which the integral is taken. (Default: 0). |
| 715 | |
| 716 | .. versionadded:: 1.7.0 |
| 717 | |
| 718 | Returns |
| 719 | ------- |
| 720 | S : ndarray |
| 721 | Laguerre series coefficients of the integral. |
| 722 | |
| 723 | Raises |
| 724 | ------ |
| 725 | ValueError |
| 726 | If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or |
| 727 | ``np.ndim(scl) != 0``. |
| 728 | |
| 729 | See Also |
| 730 | -------- |
| 731 | lagder |
| 732 | |
| 733 | Notes |
| 734 | ----- |
nothing calls this directly
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